Great pseudorhombic prismatotesseract

Great pseudorhombic prismatotesseract
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Gapript
Elements
Cells	32 triangular prisms, 24 octagrammic prisms, 8 quasitruncated hexahedra
Faces	64 triangles, 48+96 squares, 48 octagrams
Edges	96+192
Vertices	96
Vertex figure	Isosceles triangular retroprism, edge lengths 1 (2), √2 (6), and √2–√2 (4)
Measures (edge length 1)
Circumradius	${\sqrt {2-{\sqrt {2}}}}\approx 0.76537$
Hypervolume	$22{\frac {3-{\sqrt {2}}}{3}}\approx 1.25820$
Dichoral angles	Quith–3–trip: 90°
	Stop–4–stop: 90°
	Quith–8/3–stop: 45°
	Trip–4–stop: $\arccos \left({\frac {\sqrt {6}}{3}}\right)\approx 35.26439^{\circ }$
Central density	-1
Related polytopes
Army	Srit, edge length ${\sqrt {2}}-1$
Regiment	Wavitoth
Conjugate	Small pseudorhombic prismatotesseract
Convex core	Joined hexadecachoron
Abstract & topological properties
Flag count	4608
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	B4, order 384
Convex	No
Nature	Tame

The great pseudorhombic prismatotesseract is a nonconvex uniform polychoron that consists of 8 quasitruncated hexahedra, 32 triangular prisms, and 24 octagrammic prisms. Two quasitruncated hexahedra, two triangular prisms, and four octagrammic prisms join at each vertex.

Gallery

Vertex coordinates

The vertices are the same as those of the regiment colonel, the sphenoverted tesseractitesseractihexadecachoron.

External links

• Bowers, Jonathan. "Category 6: Sphenoverts" (#224).

• Klitzing, Richard. "gapript".